Intravaginal devices such as tampons and pessaries generally employ a withdrawal cord to help users remove the devices after use. Typical withdrawal cords comprise flexible materials that are unwound from a supply. Most modern manufacturing lines operate at a fairly high throughput rate. And raw materials and components are often incorporated into such manufacturing lines in the machine direction. This can also be true for intravaginal device withdrawal cords. As sections of withdrawal cord are unwound and routed in the machine direction, a length of withdrawal cord needs to be accumulated and separated from the withdrawal cord supply for attachment to an intravaginal member. Accumulating the length of withdrawal cord while the intravaginal member to which it will be attached is moving at high rates in the machine direction can be difficult. Embodiments of the present invention address this challenge.